grotendorst



Jan. 25, 1927. 1,615,510

W. F. GROTENDORST TABULAR CALCULATING APPARATUS PARTICULARLY FOR USE INTHE LAYING OF ORDNANCE Original Filed March 29 1926 I5 Sheets-Sheet 1fluenrr: 2M1, G rozznolorsif,

Jan. 25 927. 1,615,510

w. F.,GROTENDORST TABULAR CALCULATING APPARATUS PARTICULARLY FOR USE INTHE LA ING C" ORDNANCE Original 11 d larch 29, 1926 3 Sheets-Sheet 2lNVEN TOR MFGroQndo -Ft, J

ATTO R N EYS 1,615,510 w F. GROTENDORST TABULAR CALCULATING APPARATUSPARTICULARLY FOR USE IN THE LAYING OF ORDNANCE Original Filed March 29,1926 3 Sheets-Sheet 5 WE Grafendora, 7

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Patented Jan. 25, 1927.

UNITED STATES 1,615,510 PATENT OFFICE.

WILLEM FREDERIK GROTENIDORST, OF HELDER, NETHERLANDS.

lABULAR-CALC ULATING APPARATUS PARTICULARLY FOR USE IN THE LAYING OFORDNANCE.

Original application filed March 29, 1926, Serial No. 88,324, and in theNetherlands November 19, 1923. Divided and this application filed August7, 1926. Serial No. 127,962.

This application is a division of my copending application Serial No.98,324, filed March 29, 1926. r

This invention relates to tabular calculating apparatus particularly foruse in the laying of ordnance. The invention is particularly intendedfor use in conjunction with the device described in the specification ofmy co-pending patent application.

The main purpose of this invention is to provide a tabular device whichshall permit of calculating the distance of an ob ect or target fromdata obtained by simultaneous observations taken from each end of aknown base line.

The present invention consists in an improved tabular calculatingapparatus comprising a logarithmic scale constituted by a series of rowsof equal lengths arranged one 29 below the other, a ruler adapted to beused with said logarithmic scale three times the length of each of suchrows and carrying an adjustable indicating mark and being uniformlygraduated to indicate lengths in terms of the length of a row as aunit,-and an anti-logarithm table for converting lengths read from theruler into the data required, said table giving a plurality of answersfor each fraction of a unit, so that when the answer is approximatelyknown the ruler need only be read to the nearest two places of decimalsin order to obtain an approximation corresponding to the use of threefigure logarithms. I

One form of the present invention is illustrated for the sake of examplein the accompanying drawings in which Fig. 1 indicates the positions oftwo observation posts and an object, and corresponds with part of theFig. 1 ofmy above mentioned co-pending patent application.

Figs. 2 to 5 show the various elements of the apparatus, which areintended to be used in combination.

Fig. 2 shows a logarithmic chart indicating angles.

Figs. 3 and 3 show an anti-logarithm 1 table for converting logarithmsinto distances.

Fig. 4 shows a logarithmic rule with cursor. v

Fig. 5 shows an indicating plate.

In Fig. 1, Z, and Z represent two observation posts provided with anglemeasuring instruments, and D represents the position of an object ortarget. The distance Z Z =b. a is the bearing angle at which the objector target is seen from Z and ,8 is the supplement of the bearing angleat which the object or target is seen from Z t is the so-called verticalangle.

The angles a and ,8 are measured simultaneously'at the posts Z and ZFrom'this we find sint whence log. Z D=log. b+log sin a-lOg sin t. (1)

From this formula the distance Z D can be calculated, which distance isnecessary for determining certain data required -for the indirect layingof ordnance, as described in the specification of my co-pending patentapplication.

The calculation of Z 1) according to the formula (1) would of course inpractice require too much time and to facilitate rapid calculation ofthis distance Z,D the apparatus which embodies the present invention isprovided, the various details of which are illustrated in the Figures 2,3, 4 and 5. By this calculating device a simple displacement of someparts, which may be done by unskilled hands, permits of immediatelyreading Z 1). The usual table of logarithms works with numbers whichmust be added or subtracted. The principle of the calculating deviceconsists of a table (one of which is shown in Figures-3 and 3*); fourrulers with transparent slide (in Figure 4 one of them is shown) and asmall transparent plate of special shape (Figureii).

In the table of angles log. sin a and log. sin tare indicated, in theruler log. I), and

in the table of distances log. Z D. This is effected in the followingway The table of angles (Fig. 2) is constituted by a number of rowsarranged under each other and provided with graduations show ing degreesand 'minutes. .The degrees and minutes are indicated by numbers underand" above the marks, namely the degrees in large type and the minutesin small type. The numbers indicatingangles greater than 90 are arrangedunder the corresponding rows, and those which indicate angles less than90 are arranged above the rows. The marl-z indicating 90 is arranged atthe top right hand corner, so that proceeding from th1s point the rowsrun from the right to the left and then downward to the next row, etc.,

above. the rows the angles decrease from- .and therefore 146 will hefound in the second row fromthe top,'the first decimal of the log. sinbeing 8 and this number 8 being found opposite said second row.

The position of the angles in the row de pends on the second and thirddecimal. of the log. sines.- It is suflicient to take the log.

sines to three places of decimals. Again taking as-example a=46 30', logsin a being 9.861 1o.

- The second and third decimal form the numher 61. The angle 46 30'should therefore be 61/100ths of the length ofa row from the left edgeof the row.

Similarly log. sin 10 20'=9.25410.

- The angle 10 20" is therefore found in the row opposite which 2 isplaced, and 54/100ths of the length of a row from the left edge of therow.

By locating the indications of the angles in this way 1t.follows that,in order to obtain log. sin log. sin t, the first decimal is obtained bysubtracting the number at the .end of that row in which angle t is foundfrom the number at the end of. that row in which angle 0 15 found, andthe sec nd and meters (or yards,

their centers,

third decimals are found by reading, by means of one of the rulersshownin Fig. 4, by what percentage of the length of a row tllile angleindications are 'separated latera y. I

A ruler by which these lateral distances are determined is'shown in Fig.4, and comprises three portions each having a length equal to the lengthof a row in the tableof angles, shown in Fig. 2, and each uniformly 7 5graduated from right to left into one hundred divisions with suitableindications for each five divisions. Above and below the graduations ofthe middle portion, other. graduations are provided together with suitable indications of distance. The last-mentioned graduations are madesuch that the distances given correspond with the logarithmic divisionsin the middle portion of the ruler, i. e. each graduation of distancesis placed opposite that mark of the logarithmic scale which denotes thesecond and third decimal of the logarithm of the distance concerned. Thedistances indicated in the ruler shown m Fig. 4 are those from 1260.(the logarithm of which is 3.100) to 1585 (the logarithm of which is3.200). It will he understood that a suitable number of "rules isprovided to cover any length of base line which it is desired to use.For instance, if another base llne is established having. a length of3758 or other unit in which'it is desired to measure range) another rulewould be provided on which 3162 (the.loga rithm of which is 3500) wouldbe indicated at the right edge or zero of the center por-. tion of theruler, and 3981 (the logarithm of which is 3.600). would be indicatedatthe 4 left edge or mark of such center portion. In order to adjusttheruler to a certain distance a transparent slide M, made for instance ofmica and provided with two indieating points is provided. In order toad'- just this slide to a given distance it is so set thatthe verticalline connecting the two in- (heating points coincides with thegraduation showing the base line used. Adjacent each portion of eachruler such as shown inFig. 4 bears-an identifying indication, the leftportion bearing the indication V+2, the central portion V+1 and theright portion V. The letter V is used, in using the apparatus, toindicate the difference between the first decimals of log sin .1

and log sin't, which is found in the table of angles Fig. 2) bysubtracting the numbers found at the ends of the rows inwhich the anglesa and t occur. ThlS difference usually constitutes the first decimal ofthe logarithm pf the range Z,D but this first decimal w1ll be one more ithe left hand portion of the ruler must be iised or one less if the nght.hand portionmustbe used.

- By ud lmg he slide upon the ruler tol tne distance Z Z and thenplacing the ruler .ther observing by the aid of the transparent plateshown. in Figure 5 which number of the ruler is found in the sameperpendicular with the angle 2? in the table of angles, there is onlydetermined, strictly speaking, the second and third decimal of log Z.,.D which is equal to log b-l-(ldg sin a-log sin is The first decimal oflog Z D is indicated in the table of distances namely at the leftopposite the rows of distances, while the num-' Three tables ofdistances are used, one for distances between 1 and 5 kilometres, onebetween 4 and 10 kilometres and one between 10 and 32 kilometres. By wayof example the table 4-10 kilometres is shown in Figures 3 and 3. Eachtable of distances is provided with two rows of numbers preferably inred (from 0-49 inclusive and from 50-99 inclusive) which as stated aboveform the second and third decimals of log Z D. Under every red number wefind under each other four members preferably in black, which indicatethe distances corresponding to these logarithms. In the drawing theusual artillery notation is followed, in which the two numbers beforethe hyphen indicate hundred of metres, and the number after the hyphenso many times 25 metres, so that for instance the notation 66--3represents a distance of 6675 metres. g

In this way two groups each having four horizontal rows of distances areformed. Opposite each of these rows a number is placed which as statedabove corresponds with V and therefore forms the first decimal of log ZD.

If the calculations are to be effected on the assumption that the base ZZ is 1403 metres for example: then that ruler is taken on which saiddistance is found, and the indicator of the mica slide is adjusted asexactly as possible to M03 metres (see Figure 4). The ruler is thenready for use. The table of angles (Fig. 2) is then placed ready for useand the table of distances (Figure 3) is attached on it for instance bymeans'of clips. The choice of which table of distances to use depends onthe distance at which-a target may be expected. In the example assumed"here this distance is between 4 kilometres and 10 kilometres. The tableof distances referring thereto is indicated in Figures 3 for use is laidin any place on the table of angles, parallel to the rows occurring onthat table. Furthermore, a transparent indicating plate (Figure 5) istaken in the right hand, and the operator then waits until the angles aand t are determined.

For the sake of clearness a concrete example will be further worked out,and it will be assumed that The operator looks up A a in the table ofangles and finds it on t e second row from the top, at one mark to theright from the 30 mark lying between 41 and 42. The ruler is thendisplaced horizontally by the left hand over the table of angles untilits indicating point is set vertically above or below the, A a i. e. 4136. He then aseertains by displacing by the right hand the transparentplate, which red number of the ruler is now vertically above thevertical angle i. e. above 8. This appears to be about 26. Below the rednumber 26 on the table of distances the distance Z D is now found.However, four distances are found there namely 42-4, 53-1, 67--0 and84-1. As a. rule there is no doubt which of these four distances is thecorrect one, because from the previous measurement the dista'nce isalready known approximately. It may therefore only occur at the firstcalculation that it is not known which of the four distances is to bechosen. If the distance is measured by a range-finder there is no doubtpossible, because although the measurement at large distances is veryinaccurate, yet at any rate its accuracy is sufiicient to indicate whichof the given four distances is correct. If no rangefinder is at hand, itis still possible by the construction of the calculating device to makethe right choice at the .first measurement. This may be done as follows:0 posite the rows on which in the table of ang es the anglesv or. and toccur numbers are indicated. In the given examples these are the numbers8 and 1. The difference V of these is taken, i. e. 7. Above the group ofnumbers to which the number read from the ruler (26) belongs isindicated V+1. Now fromthe four distances, that one. must be chosenwhich belongs to the horizontal row opposite which is the number V+1, inthe given case 7+1=8. The correct distance is therefore 67-0, i. c. 6700m; In practice the use of the calculating device is very simple. It onlyconsists in displacing with one hand the ruler and with the other handthe mica plate.

I claim:

A tabular calculating apparatus comprising a logarithmic scale having aseries of rows of equal length and arranged one below the other, eachrow being indicated by a numeral, and having anti-logarithm indicationseach located in that row indicated portion thereof of the same length asa row of said-scale graduated into .one'hundred equal divisions adaptedwhen an antilo arithm' thereof representing a factor is adby the firstdecimal of its logarithm and.

jacent the antilogarithm of another factor on a row of the tabular scaleto determine on the rule certain logarithmic characteristics of thefinal factor by the intersection of a line projected from anantilogarithmic factor on another row of the tabular scale.

In testimony whereof I have. signed my name to this specification.

' WILD-1H FREDERlK GRO'I'ENDORST.

